Distributed ledgers and related data storage techniques, such as block chain technology, have greatly improved the ability to track transactions and other data securely in a transparent and readily verifiable manner. Block chain technology, however, remains limited in its usefulness because of its inherently extensive demands on computing power; verification of chains of transactions via hashing and public key cryptographic algorithms, and creation of new entries on such chains by similar processes, uses many computing clock cycles, which in turn results in costly degrees of consumption of energy and sometimes in lengthy wait times. Solutions thus far have implicitly proposed trade-offs between security and efficiency, for instance by using expedited processes that review portions of chains on a heuristic basis, skipping or deferring until later the review of entire chains to ensure the integrity of the process. The high degree of certainty required for the ledgers, however, means that such tradeoffs are not optimal, and generally must be supplemented with the same expensive processes originally used.